A056093 Number of 5-element ordered antichain covers of an unlabeled n-element set.
30, 2176, 54036, 709956, 6290051, 42606671, 237197942, 1135834242, 4823607212, 18563958502, 65783057592, 217240417628, 674884181813, 1987124979703, 5579019610088, 15010371955248, 38862554420034, 97163223921924, 235290234202584, 553296290481584
Offset: 4
Keywords
References
- V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
Links
- G. C. Greubel, Table of n, a(n) for n = 4..1000
- K. S. Brown, Dedekind's problem
- V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
- V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.
- Eric Weisstein's World of Mathematics, Antichain covers
Crossrefs
Programs
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Mathematica
Table[Binomial[n+30,30]-20 Binomial[n+22,22]+60 Binomial[n+18,18]+ 20 Binomial[n+16,16]+ 10 Binomial[n+15,15]-110 Binomial[n+14,14]- 120 Binomial[n+13,13]+ 150 Binomial[n+12,12]+ 120 Binomial[n+11,11]- 240 Binomial[n+10,10]+ 20 Binomial[n+9,9]+ 240 Binomial[n+8,8]+ 40 Binomial[n+7,7]- 205 Binomial[n+6,6]+ 60 Binomial[n+5,5]- 210 Binomial[n+4,4]+ 210 Binomial[n+3,3]+ 50 Binomial[n+2,2]- 100 Binomial[n+1,1]+ 24 Binomial[n,0],{n,4,30}] (* Harvey P. Dale, Sep 06 2011 *)
Formula
a(n)=C(n + 30, 30) - 20*C(n + 22, 22) + 60*C(n + 18, 18) + 20*C(n + 16, 16) + 10*C(n + 15, 15) - 110*C(n + 14, 14) - 120*C(n + 13, 13) + 150*C(n + 12, 12) + 120*C(n + 11, 11) - 240*C(n + 10, 10) + 20*C(n + 9, 9) + 240*C(n + 8, 8) + 40*C(n + 7, 7) - 205*C(n + 6, 6) + 60*C(n + 5, 5) - 210*C(n + 4, 4) + 210*C(n + 3, 3) + 50*C(n + 2, 2) - 100*C(n + 1, 1) + 24*C(n, 0).
Extensions
More terms from Harvey P. Dale, Sep 06 2011